For determining and/or monitoring a predetermined material level in a container, a material level sensor is used which contains a mechanical oscillatory structure that is mounted at the height of the predetermined material level in such a way that it comes into contact with the material when said material reaches the predetermined material level. The mechanical oscillatory structure is excited to oscillations with its natural resonance frequency. When the oscillating structure oscillates in air, it has a higher natural resonance frequency than when it is in contact with the material. This phenomenon is used for determining and/or monitoring the predetermined material level. An evaluation device compares the instantaneous frequency of the output signal of the amplifier circuit, which is always identical to the current natural resonance frequency of the mechanical oscillatory structure, with a nominal frequency, which is identical to the natural resonance frequency of the mechanical oscillatory structure when it oscillates in air, and which, for example, is recorded during manufacture or during the installation of the material level sensor. When this instantaneous frequency falls below the nominal frequency by more than a predetermined difference, it is presumed that the mechanical oscillatory structure is in contact with the material, while otherwise it is presumed that the mechanical oscillatory structure is oscillating in air. When a maximum material level is being monitored (overfill protection) the first case means that the material level to be monitored in the container has been reached or exceeded, and the second case means that the material level to be monitored in the container has not yet been reached. When a minimum material level is being monitored, on the other hand, the first case means that the material level to be monitored in the container has not yet been reached, and the second case means that the material level to be monitored in the container has been reached, or that the material has fallen below this level.